Time, Causality, and the Quantum Theory

Henry Mehlberg

Henry Mehlberg, Robert S. Cohen

H. S. Perlman

It is shown that quantum mechanics is, like thermodynamics, a phenomenological theory i.e., not a causal theory, ( not because it is a statistical theory - statistical theories with caused probability distributions can be regarded as causal) but because pure states, i.e., probability distributions of measurement values, cannot inhere in elementary particles and therefore cannot change when their world tubes intersect and hence they cannot be regarded as interacting causally. By a causal theory is meant a theory that specifies the changes in time of the states of causally interacting entities in its domain. The areas in quantum mechanics in which causal interactions are relevant include, though not explicitly, measurement and therefore the Born rule, and, explicitly, the unitary Schrodinger time development of states. The Born rule probabilities are shown to to refer not to conjoint superpositions of eigenstates but to classical mixtures of mutually exclusive eigenvalues and the Schrodinger time development of states is shown to refer to the time development of the states of non-causally interacting elementary particles and hence cannot be regarded as as a causal time development equation, appearances to the contrary notwithstanding. The recognition that quantum mechanics is not a causal theory but a phenomenological theory like thermodynamics does not affect the way it is employed to calculate an predict and hence preserves its empirical success but it does allow a typically simple phenomenological theory explanation of entanglement and other apparently non-local phenomena.

Luke Mrini, Lucién Hardy

Time-reversal symmetry is a prevalent feature of microscopic physics, including operational quantum theory and classical general relativity. Previous works have studied indefinite causal structure using the language of operational quantum theory, however, these rely on time-asymmetric conditions to constrain both operations and the process matrix. Here, we use time-symmetric, operational probabilistic theory to develop a time-symmetric process matrix formalism for indefinite causal structure. This framework allows for more processes than previously considered and a larger set of causal inequalities. We demonstrate that this larger set of causal inequalities offers new opportunities for device-independent certification of causal non-separability by violating new inequalities. Additionally, we determined that the larger class of time-symmetric processes found here is equivalent to those with Indefinite Causal Order and Time Direction (ICOTD) considered by Chiribella and Liu, thereby providing a description of these processes in terms of process matrices.

Lucien Hardy

This is a book about operational probabilistic theories. The standard approach in such theories is from a time forward perspective. In this book we mostly take a time symmetric perspective. This presents a branding problem. Is this a niche book merely about time symmetry? No. This is a comprehensive book about operational probabilistic theories, but mostly from a time symmetric perspective. In fact, this book consists of (1) a simple book about simple operations having simple causal structure (where all the inputs are before all the outputs), and (2) a complex book about complex operations that can have complicated causal structure (a complex operation is equipped with a causal diagram). For the simple case we are able to show that the time symmetric perspective is equivalent to the time forward perspective. In each book we set up (A) operational probabilistic theories (OPTs) in terms of operations, (B) Operational Quantum Theory (OQT) in terms of operator tensors which correspond to operations, and (C) the theory of Hilbert objects which can be doubled up to give operator tensors. Operations are required to be physical which guarantees that circuits built out of operations have probabilities between 0 and 1 and that certain causality conditions are met. We prove that when we wire together operations the resulting networks are also physical. We model Sorkin's impossible measurements with complex operations and show that physicality prevents anomalous signalling. We develop diagrammatic notation for Hilbert objects. This includes mirrors for doubling up and mirror theorems. We use this framework to prove time symmetric causal dilation theorems for various causal diagrams.

Henry F. Birkenhauer